B$.6$ A uniform rectangular gate $AB$ of $3m$ long and $1\mathrm{.}5m$ wide in Fig B$.6$ below is hinged at A and inclined at $40$ to horizontal. The depth of diesel oil on the left side of the gate is $3\mathrm{.}7m.$ The depth of seawater on the right side of the gate is $1m.$ Determine the self$-$weight of the gate in order to keep the gate closed. The density of seawater is $1025k\frac{g}{m^3}$ and the density of diesel oil is $875k\frac{g}{m^3}.$

$(20$ marks$)$

Fig. B$.6$